Finite Group Databasebeta

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C3×D5×C19×C11⋊C5 #44535478

order31350
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C19 · Schur multiplier (H2) = C1

Aliases

direct productC3×D5×C19×C11⋊C5
unambiguous semidirect productC5⋊(C2×C3×C19×C11⋊C5)
unambiguous semidirect product(D5×C11)⋊(C3×C5×C19)
unambiguous semidirect product(C3×D5×C11)⋊(C5×C19)
unambiguous semidirect product(C3×D5×C11×C19)⋊C5

Splittings

Fitting, socleC3×C5×C11×C19 ⋊ C2×C5
derivedC5×C11 ⋊ C2×C3×C5×C19
HallC3×C5×C19×C11⋊C5 ⋊ C2
HallC5×C19×C11⋊C5 ⋊ C2×C3
HallC3×C5×C11⋊C5 ⋊ C2×C19
HallC3×C11×C19 ⋊ C5×D5
HallC5×C11⋊C5 ⋊ C2×C3×C19
HallC11×C19 ⋊ C3×C5×D5
HallC3×C11 ⋊ C5×D5×C19
SylowC11 ⋊ C3×C5×D5×C19

Subgroups

subgroupG/H
center, hypercenterC3×C19D5×C11⋊C5
commutator, cosocle, hypocenterC5×C11C2×C3×C5×C19
FrattiniC1G
Fitting, socleC3×C5×C11×C19C2×C5
LCSG ▷ C5×C11
UCSC1 ◁ C3×C19

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3135

Conjugacy classes & character table

1596 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31350, 51);